The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  1  1  1  0  1  2  0  0  1  0  1  0  1  1  1  1  0  2  1  1  0  1  1  0  2  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  2  2  2  1  1  3  1  0  0  2  1  3  0  2  3  3  2  1  1  2  2  0  3  2  1  0  0
 0  0  1  1  1  0  1  0  1  1  0  2  1  1  1  0  1  0  0  1  1  1  1  0  2  1  2  0  1  3  1  1  1  1  1  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  0  0  0  0  2  2  2  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  0  0  2  0  2  0  2  0  0  2  0  0  2  2  2  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  2  2  0  2  2  0  2  0  2  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  0  2  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  2  2  2  2  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  0  0  2  2  2  2  0  2  2  0  2  0  2  2  0  2  2  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  2  0  2  2  0  0  0  2  0  2  2  0  2  2  2  2  0  0

generates a code of length 40 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+120x^28+42x^29+185x^30+190x^31+402x^32+424x^33+634x^34+744x^35+899x^36+1162x^37+1146x^38+1494x^39+1302x^40+1536x^41+1273x^42+1248x^43+990x^44+766x^45+597x^46+362x^47+323x^48+152x^49+212x^50+56x^51+55x^52+14x^53+40x^54+2x^55+4x^56+9x^58

The gray image is a code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.16 in 17.6 seconds.